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Barlett’s Formula for Non Linear Processes

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  • Christian Francq

    (Crest)

  • Jean-Michel Zakoïan

    (Crest)

Abstract

A Bartlett-type formula is proposed for the asymptotic distribution of the sample autocorrelations ofnonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as thesum of two terms. The first term corresponds to the standard Bartlett’s formula for linear processes,involving only the autocorrelation function of the observed process. The second term, which is specificto nonlinear processes, involves the autocorrelation function of the observed process, the kurtosis of thelinear innovation process and the autocorrelation function of its square. This formula is obtained under asymmetry assumption on the linear innovation process. An application to GARCH models is proposed.

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2008-05.

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Length: 18
Date of creation: 2008
Date of revision:
Handle: RePEc:crs:wpaper:2008-05

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Cited by:
  1. Francq, Christian & Zakoian, Jean-Michel, 2009. "Bartlett's formula for a general class of non linear processes," MPRA Paper 13224, University Library of Munich, Germany.
  2. Christian Francq & Roch Roy & Abdessamad Saidi, 2011. "Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(6), pages 699-723, November.

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